All Sunburst material is copyrighted. However, Sunburst does give the purchaser the
• You have permission to reproduce any student worksheets in this guide for your
classroom use. You should not, however, copy the whole guide.
• If you purchased this program for one computer, you may use it on a single
• If you wish to use this software on multiple computers, you must purchase the
right to do so from Sunburst. Call and ask for lab pack/site licensing prices.
• You have permission to use lab packs/site licenses within one site. You do not,
however, have permission to divide the package and use the software in more
than one site.
ThomasC. O'Brien, Ph.D.
Carrie Gerard i
Salti re Software, Inc.
Carrie Gerard i
Gregory Sill ins
Copyright © 1998 Sunburst Communications, Inc.
TI-GRAPH LINK is a trademark of Texas Instruments Incorporated.
Windows and Windows NT are registered trademarks of M icrosoft Corporation
in the U nited States and/or other countries.
For more information or for a free catalog, call or write:
Sunburst Communications, Inc.
101 Castleton Street
Pleasantville, NY 10570
Or call collect: 914-747-3310
Visit us on the Web: www.SU N BU RST.com
Table of Contents
A bout the A uthor 1
I ntroduction 3
H ardware and Software Requirements 5
Installing Puzz/e 7an/cs on a T 1-73 5
Welcome to Puzzle Tanks 7
Finding Your Way A round PuzzleTanks 9
How to Play 10
Levels of Play 10
Impossible Problems 12
Champion List 12
Error Recovery Instructions for the T 1-73 15
M iscellaneous 16
Technical Support 16
About the Author
Thomas C. O'Brien, Ph.D.
Thomas C. O'Brien is a former professor at Southern Illinois University,
Edwardsville, Illinois. His work in education is three-fold: teacher education,
curriculum development and research on children's thinking. Asa researcher, he
has studied the growth of mathematical ideas in subjects from pre-school to
medical school and law school. Asa teacher, he has worked with students from
the seventh grade through graduate school. Asa curriculum developer, he has
written twelve math-problem books for children, as well as written and edited
some eighty papers on children's thinking and education published through the
Teachers' Center Project.
In addition, Dr. O'Brien has published and delivered some 100 papers on chil-
dren's thinking, mathematics education, intellectual development and educa-
tional change. H is papers and presentations have taken place in the U nited
States, Canada, Great Britain, Holland, France, Switzerland, Hungary and
Brazil. Dr. O'Brien was named a North Atlantic Treaty Organization (NATO)
Senior Research Fellow-in-Science in 1978. He received his bachelor's degree
from lona College, New Rochelle, NY, and his Ph.D. from New York University.
Other Sunburst programs designed by Thomas O'Brien include: Teasers by
Tobbs, Tobbs L earns A Igebra, TheK ing's R ule, TheR oyal R ules, B lockers and
Finders, Blockers and Finders II, W inker's W orld of Patterns, Winker's World of
N umbers, M ore Teasers by Tobbs, Teasers by Tobbs with Integers and L abel L and.
Suppose you have the following problem:
You have two tanks, one of which holds 5 quarts and the other 6.
You have an infinite supply of Wonder Juice and a holding con-
tainer into which you could pour the contents of the tanks. You
must use the original tanks — the 5 and 6 — to make 11 quarts
of Wonder Juice.
Easy. Fill the 5 and the 6 and empty them into the holding tank.
Why do a problem like this? Such a problem calls for children to develop and/or
apply addition skills and to view addition in its very essence. Addition is not
reciting responses from memory. Addition involves combining things.
Here's another problem:
Suppose you have the same 5 and 6 tanks and this time you need
2 quarts of Wonder Juice. Not so easy, is it? You could fill the 6
and pour it into the 5, thus leaving 1. Save the 1 in the holding
container. Then empty the 5. Can you finish the problem?
This isn't an exercise in addition facts. What is it? It's problem solving, one of
the most important abilities one can have.
Problem solving takes place when one reassembles (or creates) actions and ideas
to achieve a goal in a new situation. We are all problem solvers every day, and
we are all more or less successful at problem solving. But problem-solving abili-
ties are too important to leave to chance and the random experiences of every-
day life. Problem solving needs special attention.
M uch of the school curriculum purports to promote problem solving. The
National Council of Teachers of Mathematics chose problem solving as its issue
for teachers to pursue in the 1980's. Present-day school children will live most of
their lives in the twenty-first century. What new issues will they face? No doubt,
facts will be important to them, but they'll meet novelty and challenge and
opportunities presently unknown to us. (Some of you are old enough to remem-
ber when Dick Tracy's wrist radio was unspeakably futuristic. Do you remember
— i t's just over 35 years ago — when a man on the moon was unthinkable? Can
you think back to the time when a computer in a private home was not so com-
A major aspect of life is novelty — dealing with new situations for which you've
not been programmed. What do you do? You create your own solutions. You
become a problem solver. Problem solving is, and should be, a major objective
in schools and the home.
But problem solving in math textbooks is often falsely named. "Problems" in
most math textbooks aren't really problems. They are computational exercises
disguised in words: "Two boys each ate 4 hamburgers...." Such activities are triv-
ial so far as problem solving is concerned, and they are trivial from the point of
view of utility. I haven't had to solve a "word problem" in the last thirty years of
my adult life, but during the same time, I have met and solved dozens of prob-
lems every day.
What does problem solving involve? H ofstadter says it nicely in Godel, Escher,
• to respond to situations flexibly;
• to take advantage of fortuitous circumstances;
• to find similarities between situations despite differences that may
• to synthesize new concepts by taking old concepts and putting them
together in new ways; and
• to come up with novel ideas.
Puzzle Tanks then, is concerned with problem solving in the H ofstadter sense. It
is concerned with children's ability — and willingness and confidence— to
make sense out of a situation and devise alternatives to reach a goal. The con-
struction of alternatives, not the repeating of pat formulas, is what thinking and
problem solving are all about.
How does PuzzleTanks create a good educational environment?
It deals with issues that are important. Problem solving is important.
It enables the student to be active— to invent ideas, to try them out and, if
necessary, to revise them. The very nature of PuzzleTanks is that players invent
solutions and revise them. M istakes, by the way, are okay. (Can you conceive of
an infant learning to walk without lots of falls at the beginning?)
It adds diversity. At each level of PuzzleTanks, what worked for the last problem
is unlikely to work for the next. Further, every individual problem has many dif-
ferent solutions. There is no such thing as "the one right way."
It has a wide variety of entry points and a high ceiling. PuzzleTanks starts with
very simple problems, such as the 5 + 6 = 11 task described earlier, but the
higher level problems have stumped some very bright, well educated people.
Thus, PuzzleTanks puts kids in real problem-solving situations with real lifelong
Hardware and Software Requirements
Make sureyou havethe following items:
• TI-GRAPH LINK™ computer-to-calculator cable. If you do not
haveaTI-GRAPH LIN K cable, call Sunburst, or order the cable
online at the T I Accessory Store (www.ti.com/calc/docs/store.htm).
• Connecting TI-GRAPH LIN K cable adapter, 9-pin to 25-pin, if
• Computer with Windows® 3.1x or Windows® 95/98 installed. (A
Windows NT® version will soon be available.)
• Puzzle Tanks software for the T I -73 on disk.
• A T 1-73 calculator.
Thingsto Check BeforeYou Begin
To make sure the batteries in your T 1-73 are in good working condition, turn on
your T 1-73. If there is a low- battery message on the screen, turn the T 1-73 off
and follow the battery replacement procedure in Appendix C of your T 1-73
Before you load Puzzle Tanks into your T I -73, verify that sufficient free space
exists in your application memory space by entering 2nd M EM, 3:Check APPs.
The first line indicates the number of free spaces available. Most applications
will take up only one space. Seethe Memory is Full instructions in the Trouble
Shooting Section for details about deleting applications.
may briefly display
simply means the
Installing PuzzleTanks on aTI-73
1. M ake sure the T I -G RA PH LINK cable is firmly connected to the calculator
and the computer and the calculator is at the home screen.
2. Start Windows and close all desktop applications that may be running
(another running application could interfere while Puzzle Tanks is updat-
ing your TI-73).
3. Select Run from the File menu (Windows® 3.1) or Run from the Start
menu (Windows® 95). In the Run dialog box, type
C :\ directoryname\ ti73puzz.exe (where directoryname is the directory to
which you downloaded the Puzzle Tanks file) and then click OK.
4. Follow the on-screen instructions to complete the installation.
Important: DO NOT interrupt the installation process. If any errors are
encountered during the installation, follow the instructions. Error Recovery
instructions are also described in the Trouble Shooting Section of this guide.
Welcome to PuzzleTanks
The following section takes you through a sample game of PuzzleTanks.
After installation is complete, find and press the
A PPS button located on the calculator below and
to the left of the down arrow. The Applications
screen will appear.
be a maximum of <3
Also, you may use
the number keys
when entering a
On the Applications screen use the arrow keys to
scroll down and highlight PU ZTA N KS or press
the number that corresponds with the PU Z-
TAN KS. In the above example, PuzzleTanks is the
third application on the calculator. In this case
pressing 3 will launch the application.
At the credits screen press any key to continue.
You will be prompted to enter your name.
fu :: l e THriKi"
EnUr your nam:
S T L! V H X Y Z ■■
addTdel I CLR | " TDIinE
U se the arrow keys to navigate among the letters
on the alphabet chart. The ADD option in the
menu bar allows you to select the highlighted let-
ters. The DEL option in the menu bar allows you
to delete the last letter selected. nee you have
finished entering your name, use the DON E
option in the menu bar to go to the M ain screen.
U se the arrow keys and the enter key to select the level of play you'd like to
start with. To familiarize yourself with the game, you may want to choose the
Beginner level first.
Once you choose the level you want, a problem will be presented. After you've
read the problem, press any key to begin solving it.
have an unlimited sup-
ply of liquid with which
to fill the tanks.
of Pow«r Punch.
Tht lanks hold
9 and 7 quarts.
Yyhw any U*y...
A solution to this problem is shown in the following steps:
FXLL|HDVE|EHTY| XriP |dpts
FXLL|HDVE|EHTY| IHP [WIS
FILLlHDVElEHTYrTH PjUFf 5
Graphic representation of
Fill the 9-quart tank.
Move the contents of the
9-quart tank into the truck.
Fill the 7-quart tank
Move the contents of the 7-
quart tank into the truck.
) B47\ |?feBU(^ACK
Fill the 7-quart tank 2 more
times, each time moving the
contents to the truck.
The congratulatory screen will appear when you solve the problem.
IUU dono CARRIE!!
YOU ™< xOLir
Pr«s any k4tv...
k 20 J
W hen you feel you have mastered the level at which you started, move on to
the next level for a greater challenge.
Finding Your Way Around PuzzleTanks
You will use the main menu bar located at the bottom of the screen to interact
with PuzzleTanks. The five keys directly below the game screen (hereafter
referred to as the M aster keys) correspond directly to the five items in the menu
bar. Filling and emptying tanks, or moving liquid between tanks, can all be
accomplished using these keys. For example, pressing the Y= key on the calcula-
tor will activate the FILL option in the menu bar.
Below is a description of each of these options.
• FILL causes a new menu bar to appear with options to fill either of
the tanks with liquid. BACK is provided to take you back to the main
menu bar if you do not wish to fill any tanks after all.
• MOVE causes a new menu bar to appear with options to move liquid
from one tank to another, or to move the liquid from one tank into the
truck. BACK is provided to take you back to the main menu bar if you
do not wish to move any liquid.
• EMTY causes a new menu bar to appear with options to empty either
of the tanks that contain liquid. BACK is provided to take you back to
the main menu bar if you do not wish to empty either of the tanks.
• IMP Indicates if a problem is impossible or not. A congratulatory
message will appear if you are correct. If the problem is possible, a mes-
sage will appear indicating the problem can be solved. In either case, you
will be charged one try in the Tries section of the screen.
• OPTS activates a dialog box offering the following choices: either
starting a new game or replaying the same game, going to the main
menu, getting directions, viewing the champion list, or quitting the
The program keeps track of the number of moves or "tries" used to solve each
problem. That number is shown along with the goal amount in a box located on
the right side of the game screen. In the Champion level, this number is record-
ed, and the player who solves the problem in the least number of tries is listed as
the champion for that problem.
How to Play
I n Puzzle Tanks, you are given the option to choose from four levels of play:
Beginner, Expert, Master and Champion. Each level increases in difficulty. The
tanks are chosen at random from 1 to 9 units; the goal amount is also chosen at
First, enter your name; then select a level of play. After you have selected a
level of play, you will be presented with a problem. Press any key to continue.
A graphic illustration of the elements in the problem will be displayed on the
screen. You can attempt to solve the problem by filling tanks, emptying tanks,
and moving liquids between the tanks or into the truck (depending on the level
of play) by using the options in the menu bar.
Levels of Play
In the Beginner level, the problems involve simple addition, subtraction and
multiplication. Here is an example:
Given a 9 and a 3, make 12
Given a 9 and a 3, make 6
Given a 9 and a 3, make 27
Given a 9 and a 3, make 21
(M ultipl ication. Three 9's.)
(M ulti pi ication and addition-Two
9's plus a 3.)
In summary, if one tank holds "a" and the other holds "b," Beginner level prob-
lems use the following formulas:
• kx a (e.g., 3 x a)
• k x a + c x b (e.g., 2 x a + 6 x b— two of one tank and
six of another tank will fill the truck)
In the expert level the problems are more challenging. Suppose you had tanks
holding units of 6 and 5, and the goal is 8. There could be a couple of different
You could do 6 - 5 eight times, emptying each of the remaining
units into the truck.
Or you could do 6 + 1 + 1.
Can you think of other solutions?
M aster L evel
A t the M aster level, the situation changes completely— there's no truck for stor-
age! ne must obtain the target amount with only the two tanks provided.
H ere's an example of a M aster problem:
tion is recog-
it's in one tank
q$ udd nil.
Th« tanks hold
3 and ! i quarts.
rr£SS any k«y...
Yoli havt only 2
tanks to work with.
You must obtain
th« i <iuart
usinS! th« 2: 'tanks.
rr«ss any k«y...
Here is a solution:
— Tri«s — I
FZLL|HDVE|EHTY| XHP |[iPT<:
Graphic representation of
!=! aQAL i
— Tri«S — I
FILL| HDVEl EHTYflNP JUVIS
Fill the 9-quart tank.
M aHAL 1
— Tri«S — I
TJ ■ — ' —
FZLLl HDVEl EHTV] XHP|DPTS
Move the contents of the 9-
quart tank to the 4- quart
ri GDAL i
— Tri«S —
FZLLrHDVEfEHTYl XHrl urTS
Empty the 4-quart tank.
ri GDmL i
— Trks —
TJ — 1 — ' —
Move the contents of the 9-quart
tank into the 4-quart tank.
! T 1 Wis
Empty the 4-quart tank and
you are left with 1 quart!
The goal wasl, so the problem was solved in five steps. Is there a solution with
C hampion L evel
Champion is the most challenging level of play. At this level, you may be pre-
sented with a problem that has already been solved by another player who is the
champion for that problem. This gives you the opportunity to try to solve the
problem in as many or fewer steps than your "opponent."
If there is no champion for the problem, it will be noted on the opening screen
describing the problem: "No one holds the championship." If there is a champi-
on for the current problem, the opening screen will give you the name of the
player holding the current championship and how many tries were required to
solve the problem.
If you succeed in getting the better score or tying the current champion, then
you become the new champion, and the score is recorded on the C hampion list.
To add an extra challenge to the Expert and M aster levels of play, some of the
problems are impossible to solve. For example, try to use a 2 and a 6 to make 1.
It can't be done. W ith a 2 and a 6, only 2, 4, 6, 8, 10, etc., are attainable goals.
In general, if the two tanks share a divisor (e.g., tanks of 3 and 9, 6 and 8, 2 and
10), only multiples of that divisor are possible. If the tanks share no common
divisor other than 1, the sky's the limit! For example, tanks of 3 and 5 can be
used to obtain 1, 2, 3, 4, etc.
The Champion List is accessible from the OPTS menu in the menu bar of each
game. It can be accessed anytime during or at the end of a game. The Champion
List holds and stores the names of the "champs" who were able to correctly
answer the Champion Level problems. The list contains the goal and tank sizes,
the names of the champs and how many tries they used to complete the prob-
tlSyTclrt r i<a1i<i:
You can scroll through the Champion List using the arrow keys on the calcula-
tor. The menu bar in the Champion List screen contains 3 options; PLAY, CLR
and CAN CL. If you see a game you would like to play, use the arrows to high-
light that game and select PLAY from the menu bar. The game will then open
and you will have a chance to become the new champion. To reset any of the
games in the Champion List back to No Champ simply use the arrow keys to
highlight the game and select CLR from the menu bar. If you only went into
the Champion List to look around, use the CAN CL option in the menu bar to
take you back to the screen where you were previously.
Error Recovery Instructions For the T 1-73
This error indicates the Flash Installer is unable to communicate with the
T 1-73. The problem is usually associated with theTI-GRAPH LIN K ™ cable and
its connection to the T 1-73 and/or to the computer. Make sure the cable is firm-
ly pushed into the calculator and the computer.
If this does not correct the problem, try a different T I -GRAPH LIN K cable and
reboot your computer. If you continue to get this error, please contact
1-800-TI-CARES (see Technical Support).
M emory is F ull
This download error appears when the T 1-73 contains one to four applications
that occupy the available 64K of space. In order to make room for another
application, you must delete one from the T 1-73. Before deleting an application
from the T 1-73, you can back it up by using the Windows Backup A pp command
in TI-GRAPH LIN K for the T 1-73. Once saved, you can reload it to the
TI-73 later using T l-G RA PH LINK.
Expiration D ate R eached
The application has reached its expiration date and can no longer be used.
Please contact 1-800-TI-CARES (see Technical Support).
M iscellaneous E rror Received
W rite down the error code displayed in the dialog box and contact
1-800-TI-CARES (see Technical Support).
Exit the installer and try it again. If this problem persists, contact
1-800-TI-CARES (see Technical Support).
Low Battery Condition
It's a good idea to make sure that you have sufficient battery power prior to
attempting a download. Low battery indication is shown on the initial screen. If
you receive this error during an installation, change the batteries before trying
If you obtain new or upgraded software for your T I -73, you may need to provide
your current software version and/or the serial number of your unit. It is also
good to know your version number in case you have difficulties with your T 1-73
and need to contact technical support. Knowing the software version may make
it easier to diagnose the problem.
Knowing the available number of application spaces in advance helps you better
manage your application downloads.
Verify M aintenance U pgrade Version
On the T I -73, enter 2nd, Mem, l:About. The version number has the format
Verify Application Version number
On the T 1-73, select A PPS. Select the appropriate application and press
ENTER. The version number of the application appears on the initial screen.
Verify Serial N umber
On the T 1-73, enter 2nd, Mem, l:About. The serial number appears on the line
beneath the product ID number.
C heck A mount of Flash A pplication Free Space
n the T 1-73, select 2nd, M EM , 3:C heck A PPs. T he number to the right of
"Spaces Free:" indicates the number of spaces available for applications. Each
application requires one space. There are a maximum of four free spaces.
For questions concerning the installation of PuzzleTankson your T 1-73
or for questions concerning the T 1-73 calculator, contact Texas Instruments
C ustomers in the U .S. t C anada, Puerto Rico and the Virgin Islands
Send use-mail email@example.com.
Call us at 1-800-TI-CARES (1-800-842-2737)
C ustomers outside theil .S. f C anada, Puerto Rico and the Virgin Islands
Send use-mail firstname.lastname@example.org.